BUCKLING ANALYSIS OF TAPERED COMPOSITE PLATES USING RITZ METHOD BASED ON FIRST-ORDER SHEAR DEFORMATION THEORY

2012 ◽  
Vol 12 (04) ◽  
pp. 1250030 ◽  
Author(s):  
SHAIKH AKHLAQUE-E-RASUL ◽  
RAJAMOHAN GANESAN
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Turbine Blades ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Width Ratio ◽  
First Order ◽  
Closed Form Analytical Solution

Tapered composite plates have various engineering applications such as helicopter yoke, robot arms and turbine blades in which the structure needs to be stiff at one end and flexible at another end. No closed form analytical solution of tapered composite plates using Ritz method based on first-order shear deformation theory (FSDT) is available at present. In the present paper, the buckling analysis of different types of composite plates with longitudinal-internal-ply-drop-off configuration is investigated using Ritz method. The buckling analysis of these plates is also conducted using ANSYS®. The efficiency and accuracy of the developed formulation are established in comparison with available solutions, where applicable. A detailed parametric study has been conducted on various taper and lay-up configurations, all made of NCT/301 graphite-epoxy, in order to investigate the effects of taper angle, length-to-height ratio, length-to-width ratio, boundary conditions, and taper and lay-up configurations.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

A Simple Higher-Order Theory for Laminated Composite Plates

1984 ◽  
Vol 51 (4) ◽  
pp. 745-752 ◽  
Author(s):  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
First Order ◽  
First Order Theory

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano [6], but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

A novel first-order shear deformation theory for laminated composite plates

2014 ◽  
Vol 17 (3) ◽  
pp. 321-338 ◽  
Author(s):  
Mohamed Sadoune ◽  
Abdelouahed Tounsi ◽  
Mohammed Sid Ahmed Houari ◽  
El Abbes Adda Bedia
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
First Order

scholarly journals First Order Shear Deformation Theory access for the stress research of CNT/Polymer Laminated Composite Plates

2019 ◽  
Vol 8 (6) ◽  
pp. 3736-3740
Keyword(s):  
Carbon Nanotube ◽  
Shear Deformation ◽  
Polymer Composite ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Theory Approach ◽  
Laminated Composite Plates ◽  
First Order

In the design of structural elements like shells, beams, and plates the analysis of stresses is one of the primary and most important considerations. The intention of the current research is to perform a study on stress behavior of laminated polymer composite plates reinforced with carbon nanotube(CNT). A theoretical first order shear deformation theory approach is executed on simply supported laminated composite plates subjected to uniformly distributed loads to study the effect of shear deformation on in-plane and transverse stresses. The numerical results are presented for symmetrical, eight layered polymer composite reinforced with Carbon Nanotube to explore the effect of various parameters like stacking sequence, the side-to-thickness ratio on stresses. The effect of carbon nanotube volume fraction and carbon nanotube radius is also investigated on stress distribution of composite plates. This study on stress analysis is conducted on plates principally to observe the structural suitability of nanocomposites.

scholarly journals Application of alternative II theory to vibration and stability analysis of thick rectangular plates (Isotropic and orthotropic)

2020 ◽  
Vol 39 (1) ◽  
pp. 52-62
Author(s):  
O.M. Ibearugbulem ◽  
S.I. Ebirim ◽  
U.C. Anya ◽  
L.O. Ettu
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequency ◽  
Deformation Theory ◽  
Thick Plate ◽  
Shape Function ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
First Order ◽  
Fundamental Natural Frequency

This work analysed the free vibration and stability of thick isotropic and orthotropic plates with SSSS and SSFS support conditions by applying the alternative II theory based on polynomial shape function. The total potential energy which was obtained by combining the strain energy and external work was reduced to three governing equations using Ritz method. Polynomial shape function which varies with Poisson’s ratio was substituted into the governing equation to obtain the fundamental natural frequency, linear frequency and critical buckling load. The values of frequencies of the first mode and critical loads obtained were compared with those obtained using first order shear deformation theory. For span depth ratio of 10, the fundamental linear frequency for orthotropic SSFS plate corresponding to modulus of elasticity ratios (E1/E2) of 10, 25 and 40 are 0.00156, 0.00219 and 0.00255Hz. The corresponding values using first order shear deformation theory are 0.00152, 0.00212 and 0.00245Hz. Keywords: Fundamental natural frequency, SSSS plate, SSFS plate, Ritz method, Orthotropic thick plate, Isotropic thick plate, Stability, Free vibration

scholarly journals A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2385 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Nguyen Dinh Quang ◽  
Do Van Thom
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Shear Stresses ◽  
Transverse Shear Strain ◽  
First Order ◽  
Advanced Composite

A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

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